{"id":140,"date":"2022-04-13T08:27:33","date_gmt":"2022-04-13T08:27:33","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=140"},"modified":"2025-11-01T05:08:25","modified_gmt":"2025-11-01T05:08:25","slug":"h-8-properties-of-kites","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/h-8-properties-of-kites\/","title":{"rendered":"H.8 Properties of kites"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Properties of kites<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3bWFCwwg\/fS3IUGweiGdHZsrp46IdEA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3bWFCwwg&#x2F;fS3IUGweiGdHZsrp46IdEA&#x2F;watch?utm_content=DAG3bWFCwwg&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-left has-text-color has-link-color has-huge-font-size wp-elements-effa86ae39b84df78cecdb5545a2590a\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\"><strong>\ud83c\udf1f Properties of Kites \ud83c\udf1f<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-311d7ec1eff2122a0e6daa19602c82bc\" style=\"color:#000060\"><strong>Definition of a Kite<\/strong> \u2708\ufe0f<\/p>\n\n\n\n<p>A kite is a <strong>quadrilateral<\/strong> with <strong>two distinct pairs of adjacent sides equal<\/strong>.<\/p>\n\n\n\n<p>Example: If a kite has sides AB = AD and BC = CD, then it is a kite.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9d1ebb91966aa79eced03c6a1e3c9eb9\" style=\"color:#000060\"><strong>Diagonals<\/strong> \u2195\ufe0f\u2194\ufe0f<\/p>\n\n\n\n<p>The <strong>diagonals of a kite are perpendicular<\/strong> (meet at 90\u00b0) \u26a1<\/p>\n\n\n\n<p>One diagonal <strong>bisects the other<\/strong> (divides it into two equal parts). \u2702\ufe0f<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-54f7595edb46558916780515956a3503\" style=\"color:#000060\"><strong>Symmetry<\/strong> \ud83d\udd37<\/p>\n\n\n\n<p>A kite has <strong>one line of symmetry<\/strong> along the diagonal that bisects the other diagonal. \ud83e\ude9e<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-20fef135590134d017b306f4b277e965\" style=\"color:#000060\"><strong>Angles<\/strong> \ud83d\udd3a<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color has-normal-font-size wp-elements-8bc82b8609cd2ab3e6c4a40b9e2ca01d\"><strong>Angles between unequal sides<\/strong> are <strong>equal<\/strong>. \u2705<\/p>\n\n\n\n<p><strong>Angles formed by the bisected diagonal<\/strong> are <strong>right angles<\/strong> (90\u00b0).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8f1f146de503bebb838453e8efde7cfa\" style=\"color:#000060\"><strong>Area of a Kite<\/strong> \ud83d\udcd0<\/p>\n\n\n\n<p>Formula: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Area = 1\/2 \u00d7 d<sub>1<\/sub> \u00d7 d<sub>2<\/sub><\/strong><\/p>\n\n\n\n<p>\u200b where d<sub>1<\/sub> and d<sub>2<\/sub> are the lengths of the diagonals.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-a3a36d5b00770f0f51160b1db53484c7\" style=\"color:#000060\"><strong>Perimeter<\/strong> \ud83e\uddee<\/p>\n\n\n\n<p>Formula: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Perimeter = 2 \u00d7 (sum&nbsp;of&nbsp;unequal&nbsp;sides)<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-245a792812d4f7fbd8d6b47b2e9e9811\" style=\"color:#000060\"><strong>Special Properties<\/strong> \u2728<\/p>\n\n\n\n<p>Two pairs of adjacent sides are equal. \ud83d\udcab<\/p>\n\n\n\n<p>Exactly <strong>one diagonal bisects the other<\/strong>. \ud83e\ude84<\/p>\n\n\n\n<p>The <strong>longer diagonal bisects the angles<\/strong> at its ends. \ud83c\udfaf<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-48522f923152f91fe1b024bfa275bd6c\" style=\"color:#000060\">\ud83d\udca1 <strong>Tip for remembering<\/strong>:<\/p>\n\n\n\n<p>Think of a kite flying in the sky: the stick (diagonal) is strong and straight, forming a cross with the tail \ud83e\ude81.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f2b7ee\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Quadrilateral HIJK is a kite. What is \u2220J?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-2-1.png\" alt=\"\" class=\"wp-image-8629\" style=\"width:320px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-2-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-2-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-2-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220J= _____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>\u2220H and \u2220J are opposite angles. Also, \u2220I and \u2220K are opposite angles.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__2_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-8630\" style=\"aspect-ratio:1;width:325px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__2_-removebg-preview-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__2_-removebg-preview-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__2_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since HIJK is a kite and \u2220I\u2260\u2220K, \u2220H=\u2220J. Use the fact that the sum of the interior angle measures of a quadrilateral is 360\u00b0 to set up an equation and solve for \u2220J.<\/p>\n\n\n\n<p>\u2220H + \u2220I + \u2220J + \u2220K = 360\u00b0<\/p>\n\n\n\n<p>\u2220J + \u2220I + \u2220J + \u2220K = 360\u00b0 Substitute \u2220H = \u2220J<\/p>\n\n\n\n<p>2 . \u2220J + \u2220I + \u2220K = 360\u00b0 Combine like terms<\/p>\n\n\n\n<p>2 . \u2220J + 138\u00b0 + 130\u00b0 =  360\u00b0 Plug in \u2220I = 138\u00b0 and \u2220K = 130\u00b0<\/p>\n\n\n\n<p>2 . \u2220J + 268\u00b0 = 360\u00b0 Combine like terms<\/p>\n\n\n\n<p>2 . \u2220J = 92\u00b0 Subtract 268\u00b0            from both sides<\/p>\n\n\n\n<p>\u2220J = 46\u00b0                                  Divide both sides by 2<\/p>\n\n\n\n<p>So, \u2220J=46\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bbfbc3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Quadrilateral RSTU is a kite. What is \u2220U?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-3-1.png\" alt=\"\" class=\"wp-image-8635\" style=\"width:338px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-3-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-3-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-3-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220U= ____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>\u2220S and \u2220U are opposite angles. Also, \u2220R and \u2220T are opposite angles.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__3_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-8636\" style=\"aspect-ratio:1;width:275px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__3_-removebg-preview-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__3_-removebg-preview-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__3_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since RSTU is a kite and \u2220R\u2260\u2220T, \u2220S=\u2220U. Use the fact that the sum of the interior angle measures of a quadrilateral is 360\u00b0 to set up an equation and solve for \u2220U.<\/p>\n\n\n\n<p>\u2220R+\u2220S+\u2220T+\u2220U = 360\u00b0<\/p>\n\n\n\n<p>\u2220R+\u2220U+\u2220T+\u2220U = 360\u00b0                        Substitute \u2220S=\u2220U<\/p>\n\n\n\n<p>\u2220R+2\u2220U+\u2220T = 360\u00b0                        Combine like terms<\/p>\n\n\n\n<p>72\u00b0+2\u2220U+46\u00b0 = 360\u00b0                 Plug in \u2220R=72\u00b0 and \u2220T=46\u00b0<\/p>\n\n\n\n<p>2 . \u2220U+118\u00b0 = 360\u00b0               Combine like terms<\/p>\n\n\n\n<p>2 . \u2220U = 242\u00b0                  Subtract 118\u00b0 from both sides<\/p>\n\n\n\n<p>\u2220U = 121\u00b0                  Divide both sides by 2<\/p>\n\n\n\n<p>So, \u2220U=121\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">\ud83c\udfcb\ufe0f\u200d\u2642\ufe0f Work it out\ud83c\udfcb\ufe0f\u200d\u2640\ufe0f<br><br>Not feeling ready yet? These can help:<br><br>\ud83e\udd4f<a href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-1-classify-quadrilaterals\/\" title=\"H.1 Classify quadrilaterals\"><\/a><a href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-3-properties-of-parallelograms\/\" title=\"H.3 Properties of parallelograms\">Properties of parallelograms<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85124\/373\/345\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45.png\" alt=\"\" class=\"wp-image-7811\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85330\/998\/866\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54.png\" alt=\"\" class=\"wp-image-7812\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Properties of kites Design by Delta publications key notes : \ud83c\udf1f Properties of Kites \ud83c\udf1f Definition of a Kite \u2708\ufe0f A kite is a quadrilateral with two distinct pairs of adjacent sides equal. Example: If a kite has sides AB = AD and BC = CD, then it is a kite. Diagonals \u2195\ufe0f\u2194\ufe0f The diagonals<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-8-properties-of-kites\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.8 Properties of kites&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-140","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=140"}],"version-history":[{"count":25,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/140\/revisions"}],"predecessor-version":[{"id":18179,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/140\/revisions\/18179"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}